Resonators of this type with small dimensions have already been disclosed in the prior art document U.S. Pat. No. 4,384,232, which is incorporated herein by reference. That document discloses a tuning fork resonator formed of a base and two vibrating arms extending from the base. Each arm carries metallised portions that form central electrodes on the main opposite surfaces and lateral electrodes along the sides of each arm. The central electrodes of one arm are connected to the lateral electrodes of the other arm and to one terminal of a power supply. The other central and lateral electrodes are connected in an identical manner to the other terminal of the power supply. The electrodes are subjected to electrical fields in order to make the arms vibrate at a desired fundamental frequency.
Grooves are provided in each arm. The arrangement of the central electrodes inside the grooves, in the thickness of the arms, increases the piezoelectric coupling. In equal dimensions, this increase in the coupling causes a decrease in the equivalent resistance for a given resonator quality factor and consequently a decrease in the power consumption thereof. This effect can be modelled as a result of the reduction in the series resistance representing losses in the equivalent conventional resonator circuit. Conversely, for the same desired equivalent resistance, this arrangement allows a reduction in the dimensions of the resonator.
These grooves are advantageously as deep as possible provided that the resonator maintains good mechanical resistance. The zones arranged between the grooves and the lateral edges of the arms must remains sufficiently rigid and must also remain connected to the central part of the arms in a sufficiently rigid manner so as to be able to make the whole of the tuning fork vibrate.
Owing to the use of these grooves, it is possible to attain a higher degree of miniaturisation, for the same given frequency and for the same given equivalent resistance. However, below a certain dimension, the decrease in volume of the elastically active piezoelectric material is associated with a decrease in quality factor, which causes an undesirable increase in the equivalent resistance.
It is thus an object of the present invention to provide a piezoelectric resonator that can be miniaturised as much as possible without causing an excessive increase in the equivalent resistance.
Moreover, a piezoelectric resonator of the type described above has a motional capacitance that can be defined as being proportional to the integral of the stresses for each resonance mode, i.e. for a fundamental frequency resonance mode, but also for harmonic frequency resonance modes and more specifically for a first partial frequency resonance mode. It is thus another object of this invention to provide a piezoelectric resonator that has a maximum motional capacitance for the fundamental frequency and a minimum motional capacitance for the partial frequency, which is the frequency that may be started accidentally by the oscillator circuit.